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DETERMINATION OF  MOLECULAR WEIGHT        33

solvent to be lowered i° by dissolving i, 2, 3 and 4 grams
respectively, of four different substances, the molecular weights
of these substances will be in the ratio of i : 2 : 3 : 4. In ordei
to convert these ratios into true molecular weights, the numbers
must be multiplied by a coefficient which depends upon the
nature of the particular solvent selected, and may be deter-                        £*

mined empirically by means of substances of known molecular                    1J \^

weight or by calculation from thermodynamical data.1                                    5"A 4

If w is the weight of substance and W^the weight of solvent,                         ''/, J

d the depression of the freezing-point, and k the coefficient for                          ''^,,

the solvent determined for the standard conditions, i.e., for the                        i" C*\

weight of substance, which produces i° depression in 100 grams                          '.'!'*'

of solvent, the molecular weight M is given by the following
expression:—                                                                                                                   «"*

If __ ! °° &W-                                                                   'I '.",',

_____                                                                     >'< ,

.' * i!»

The values of k for some of the common solvents with their                  *           $

melting-points are given in the following table :—•                                                     ' ^

|    m.p.
Water...         .........    !     o°

Nitrobenzene
Benzene
Acetic acid
Phenol...

5"3

5'4
17
40

/-Toluidine    .........    I    42*5

39 -o
72'°

It should be remembered that nitrobenzene, phenol, and acetic acid
are hygroscopic.
The following apparatus is required :—
A Beckmann Freezing-point Apparatus.—The form of appar-
atus is shown in the accompanying Fig. 30. It consists of a
glass jar standing on a metal tray and furnished with a stirrer.
The cover of the jar has a wide slit to admit the stirrer, and a
circular aperture with clips to hold a wide test-tube.
Within the wide test-tube is a narrower one, which is held in
position by a cork. The narrow test-tube is sometimes
*
1 Vide van't Hoflf, Ztscltr, pkys. Chcm., 1. p. 481 ; Ostwald, Outlines of General
Che»tistry} chap. vi. p. 139 ; J. Walker, Introduction, to Physical Chemistry, chap*
xviii. p. 176.
,COHEN'S ADV. P. o. c.                                            D